Engineering Critical Assessment ofBuckle Arrestor

Master Thesis

Ning Wu

SupervisorProf.Dr.A.V.Metrikine

Dr.Ping LiuDr.ir.Michael JanssenDr.ir.F.P.van der Meer

Abstract

In the deep water S-lay installation, the buckle arrestor rolls on and drops off therollers repeatedly when it moves along the stinger. When the buckle arrestor islocated on the roller, there is strain intensification at the 12 o’clock position of thepipe section which is close to the buckle arrestor, and the strain can reach 1%.When the buckle arrestor drops off the roller, the strain decreases. The maximumstrain occurs around the position where the girth welding is located, a defective girthwelding part may fail under this cyclic loading. If an initial flaw exists, it is im-portant to be able to predict the total crack growth under the cyclic loading process.

The thesis is conducted in three stages. In the first stage, the global FE modelis used to model the buckle arrestor behavior during its passage over the stinger,especially the bending moment variation. In the second stage, the output from theglobal model is used as input for the local FE model, to obtain the stress and strainof the pipe cross section. In the third stage, based on the local output, EngineeringCritical Assessment is carried out on the girth welding part. The girth weldingsafety is judged by comparing the predicted crack growth with the limit standard.

It is found out that the buckle arrestor is safe under realistic cyclic loading con-ditions. This is due to the relatively small strain range which causes little influenceon the fracture resistance. The total crack growth can be treated as superpositionof tearing growth and fatigue growth.

While when large cyclic strain range is applied, according to some experiments andnumerical results, the simplified superposition method is not suitable anymore. Thecompressive loading could reduce the crack tip fracture resistance. In that case, aproper evaluation of the fracture resistance under the large cyclic loading conditionsbecomes necessary. Further systematic study should be carried out on the mutualeffects of tearing growth and fatigue growth.

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Contents

1 Introduction 11.1 General Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Objective of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Method of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Global S-Lay Installation Analysis 42.1 S-Lay in OFFPIPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.1 General Introduction . . . . . . . . . . . . . . . . . . . . . . . 42.1.2 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 FE Global Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.1 Base Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.2 Modeling with Time Loading History . . . . . . . . . . . . . . 92.2.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . 12

3 Buckle Arrestor Local FE Analysis 163.1 Static Modeling Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.1.1 Former Study . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.1.2 Simplified Model . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2 Cyclic Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4 Theory of Engineering Critical Assessment 194.1 Critical Concepts in Fracture Mechanics . . . . . . . . . . . . . . . . 19

4.1.1 J-Integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.1.2 Crack Tip Opening Displacement . . . . . . . . . . . . . . . . 204.1.3 Stress Intensity Approach . . . . . . . . . . . . . . . . . . . . 20

4.2 Method of Engineering Critical Assessment . . . . . . . . . . . . . . . 214.2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.2.2 Defining Loads and Stresses . . . . . . . . . . . . . . . . . . . 214.2.3 Nonlinear Stress-Strain Curve . . . . . . . . . . . . . . . . . . 224.2.4 Defining Fracture Resistance . . . . . . . . . . . . . . . . . . . 224.2.5 Characterize the Flaw Size and Shape . . . . . . . . . . . . . 234.2.6 Selection of Failure Assessment Diagram . . . . . . . . . . . . 234.2.7 Calculation of the Load Ratio Lr . . . . . . . . . . . . . . . . 234.2.8 Calculation of the Fracture Ratio Kr . . . . . . . . . . . . . . 23

4.3 Ductile Tearing Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 244.3.1 Ductile Tearing Mechanism . . . . . . . . . . . . . . . . . . . 244.3.2 Ductile Tearing Instability . . . . . . . . . . . . . . . . . . . . 254.3.3 Ductile Tearing with Failure Assessment Diagram . . . . . . . 25

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4.4 Fatigue Crack Growth Assessment . . . . . . . . . . . . . . . . . . . . 284.4.1 Fatigue Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 284.4.2 General procedure of assessment . . . . . . . . . . . . . . . . . 29

5 Crack Growth Estimation 315.1 Description of Simplified Method . . . . . . . . . . . . . . . . . . . . 315.2 Ductile Tearing Growth . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.2.1 General Calculation Procedure . . . . . . . . . . . . . . . . . . 315.2.2 Assumption 1 - History Independent R Curve . . . . . . . . . 335.2.3 Assumption 2 - Material Memory R Curve . . . . . . . . . . . 345.2.4 Assumption 3 - History Dependent R Curve . . . . . . . . . . 37

5.3 Fatigue Crack Growth . . . . . . . . . . . . . . . . . . . . . . . . . . 38

6 Literature Review and Results Analysis 416.1 Previous FEM Research . . . . . . . . . . . . . . . . . . . . . . . . . 416.2 Similar Experiments Study . . . . . . . . . . . . . . . . . . . . . . . . 44

6.2.1 Case One . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446.2.2 Case Two . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6.3 Results Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496.4 Future FE Study Proposal . . . . . . . . . . . . . . . . . . . . . . . . 49

6.4.1 Global Physics Summary . . . . . . . . . . . . . . . . . . . . . 496.4.2 FE study Proposal . . . . . . . . . . . . . . . . . . . . . . . . 50

7 Conclusions 53

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Notation

CTOD Crack Tip Opening DisplacementK Stress Intensity FactorE Young’s modulusσt True stressεt True strainKmat Critical Stress Intensity Factorδmat Fracture toughness in terms of CTODLr Load ratioσref Reference stressσy Yield stressKr Fracture ratioKI,p Applied stress intensity factor due to primary loadsKI,s Applied stress intensity factor due to secondary loads∆K Stress intensity factor rangeρ Plastic interaction effectECA Engineering Critical Assessment

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Chapter 1

Introduction

1.1 General Background

The applications of offshore pipeline gradually move towards ultra deep water, aconsiderable amount of work needs to be done to ensure pipeline safety during fab-rication, installation and operation phases. These force engineers to deepen thedevelopment in the design stage. In the engineering industry, some standard codeslike the DNV-OS-F101 have published the relevant limit state design criterion. Themarine pipeline system should be designed against these potential failure modes:Serviceability Limit State, Ultimate Limit State, Fatigue Limit State, AccidentalLimit State [3].-Serviceability Limit State describes a condition, if exceed, the pipeline normal op-erations will be influenced. Usually it emphasizes on local damage, unacceptabledeformations, etc.-Ultimate Limit State represents a situation, if exceed, the integrity of the pipelinewill be destroyed. For instance, bursting, plastic collapse, etc.-Fatigue Limit State means the fatigue crack growth of a structure under cyclicloading.-Accidental Limit State describes excessive pipeline damage as a result of accidents,like dragging anchors, extreme waves, etc.

The South Stream Transport B.V. is planning to build a new gas pipeline systemacross the Black Sea. The pipeline system contains four offshore 32-inch pipelines.The total length is about 930 km. The maximum water depth reaches 2200 m.

1.2 Objective of Thesis

In order to avoid the pipeline from buckling, especially in deep water section, every2000 m a buckle arrestor is positioned. During the S-Lay installation phase, thebuckle arrestor will pass over the stinger, it goes on and drops off the roller-boxes inseveral cycles. When the buckle arrestor is located on the roller-box, at 12 o’clockposition of the pipe section which is close to the buckle arrestor, there will be strainintensification. Especially when the water depth reaches 2200 m, the local strainis quite high and can approach nearly 1%. When the buckle arrestor drops off the

1

roller-box, due to the unloading, the strain intensification reduces.

The strain intensification area is the position where the girth welding is located,as illustrated in Figure 1.1. In reality, the welding part is not perfect, flaws alreadyexist. Thus in this situation, the buckle arrestor passes over the roller-boxes repeat-edly, the girth welding part will experience the cyclic loads. If there is a surface flawat 12 o’clock position of the girth welding part, under these cyclic loadings, the finalcrack growth may exceed the allowable limit. For instance, the maximum allowablecrack growth is 1 mm. Once it exceeds, it will be dangerous for the following instal-lation and the future operation activities.

Figure 1.1: Sketch of the buckle arrestor

Detailed analysis must be carried out to predict the total crack growth under thecyclic loading history. First, the cyclic loads on the buckle arrestor during its pas-sage over the stinger will be evaluated properly. Then according to the identifiedloads, the Engineer Critical Assessment is carried out on the defective girth weldingpart. The predicted total crack growth is compared with the limit standard. If itis within the limit state, then the buckle arrestor is safe. If it exceeds the allowablecrack growth, the buckle arrestor will be dangerous, further work need to be donein the pipeline design phase.

1.3 Method of Thesis

The global analysis is conducted in the first stage, the FE modeling is used to identifythe buckle arrestor global behaviors. The typical static FE modeling is reproduced.Also a modified FE model is created to investigate the stress, the strain and thebending moment variations under the proper time loading history.

Because of the beam element type, the mesh size and the model scale, the global FEmodel could not catch the pipe cross section behavior. Therefore a local FE modelis created in the second stage. The model scale is reduced, the local geometry isspecified, the 3D solid element is used, and the mesh size is refined. The global out-put will be used as input for the local FE model to obtain the local strain and stress.

2

In the third stage, based on the obtained local strain and stress, the EngineeringCritical Assessment is carried out on the girth welding part. Both ductile tearingand fatigue growth are evaluated to predict the total crack growth. According tothe previous similar FE research and experiments study, the predicted crack growthis compared with the limit standard.

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Chapter 2

Global S-Lay Installation Analysis

2.1 S-Lay in OFFPIPE

2.1.1 General Introduction

In deep water pipeline S-Lay installation, the required curvature of stinger sectionis quite high, and the departure angle could reach to 70 ◦ or even more. The depar-ture angle means the angle when pipe slides off the stinger, usually the second tolast roller. The objective of the large departure angle is to avoid over-high strainintensification on the pipe at the departure roller-box. When pipe follows the highstinger curvature, the overall high top tensile strain increase plastic deformationat 12 o’clock location [11]. And the discontinuous roller-boxes support reactionsincrease the pipe local curvature which lead to higher local bending moment. Asa result, the local strain of the pipe at the support positions are much higher thanother locations. Figure 2.1 and Figure 2.2 are examples that illustrate the phe-nomenon. Some industry criteria like DNV OS F-101, ASME VII, have defined therelevant limit states criterion for the over-bend strain to insure the safety duringinstallation phase.

Figure 2.1: Bending Moment Variation of S-Lay

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Figure 2.2: Bending Strain in S-Lay

2.1.2 Case Study

OFFPIPE is a classical software to model offshore pipeline installation and oper-ation. It is based on the nonlinear finite element method. The classical Euler-Bernoulli beam theory is used to analyse offshore pipeline and cable structures,including static and dynamic situations.

The case study is based on the South-Stream Project. Static analyses of the 2200m water depth S-Lay are performed in the OFFPIPE(2.06). The pipe diameter is32-inch and the wall thickness is 39 mm. The steel material grade is X65 and theconcrete coating is neglected. The singer radius is 140 m, and the fixed-end beamelement is used to model the stinger. The stinger geometry is defined by specifyingx coordinate and y coordinate of the stinger nodes explicitly. Three dimensionalsimple support is used to restrain pipe lateral displacement. And the support prop-erty is presented by defining the roller stiffness.

According to the definition of the OFFPIPE, the roller-bed length means the ef-fective contact length between pipe face and roller-box face. Three cases are in-vestigated based on the different roller-bed lengths, including single node support,roller-bed length of 1 m, roller-bed length of 7 m which nearly covers the whole spanbetween two stinger nodes. The Figure 2.3 illustrates them.

Figure 2.3: Roller-boxes Modes

Static analyses have been carried out on these three modes. The bending moments

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and strains at the stinger nodes of these three cases are shown in Table 2.1 and Table2.2 respectively. According to the results, increasing the roller-bed contact lengthcould reduce the local bending moment and strain concentration. At the departureroller-box, the moment is highest. Especially when the support reaction become asingle node force, the strain could reach 0.414%. This strain is quite high and thefracture assessment should be carried out [3]. This feature has been proved in manypractical S-Lay projects, especially in deep water installation. By covering the spanbetween two roller-boxes to increase the contact area, lower strain concentration willappear on the pipe section.

Table 2.1: Bending Moment Variations along Stinger Nodes

Bending Moments (kN.m)tingerNodes

Roller-bedLength(0 m)

Roller-bedLength(1 m)

Roller-bedLength(7 m)

1 9468.5 9386.6 8878.92 9048.9 9005.3 8734.53 9138.9 9081.2 8723.44 9056.3 9005.2 8688.35 9242.8 9181.6 8802.16 9107.7 9056.4 8738.47 9129.5 9075.9 8743.98 9092.3 9039.4 8711.19 9112.6 9058.1 8719.910 9075.4 9025.4 8715.311 9207.2 9148.5 8784.612 9246.4 9183.9 8821.513 9076.2 9026.5 8783.414 9473.5 9351.9 8652.715 4868.3 4868.3 4868.316 2523.7 2523.7 2523.717 1308.5 1308.5 1308.5

2.2 FE Global Modeling

2.2.1 Base Model

General

In deep water pipeline installation, in order to prevent pipe from buckling, withina certain length, a buckle arrestor is positioned. When the buckle arrestor passesover the stinger, due to the increase of wall thickness, the reaction force will behigher when the buckle arrestor is positioned on the roller-box. As a result, the

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Table 2.2: Total Strain Variations along Stinger Nodes

Total Strains (%)tingerNodes

Roller-bedLength(0 m)

Roller-bedLength(1 m)

Roller-bedLength(7 m)

1 0.414 0.399 0.3322 0.351 0.345 0.3183 0.362 0.354 0.3174 0.351 0.345 0.3145 0.376 0.368 0.3246 0.358 0.351 0.3187 0.360 0.353 0.3188 0.356 0.349 0.3169 0.358 0.351 0.31710 0.353 0.347 0.31611 0.371 0.363 0.32212 0.376 0.367 0.32613 0.353 0.347 0.31814 0.414 0.393 0.31015 0.170 0.170 0.17016 0.105 0.105 0.10517 0.072 0.072 0.072

local bending moment increases with respect to the average bending moment of thepipe sections. Higher strain intensification will appear at 12 o’clock position of thepipe sections which are close to the buckle arrestor. And that is the place wheregirth welding part is located. Detailed analysis must be carried out to ensure thatthe strain intensification will not exceed the allowable value.

Several numerical studies have been carried out on this phenomenon. Typically,by replacing part of the pipe section with the buckle arrestor at the certain locationwhich corresponding to the roller-box under investigation. Then external loads areadded to let them follow the stinger profile. Usually the departure roller positionwhere the maximum strain intensification appears is assessed. If the strain satisfiesthe fracture assessment, the pipe is considered safe.

However, the strain intensification area is the place where girth welding is located.In reality, defects exist in the girth welding before installation. During installation,the buckle arrestor goes on and drops off the roller-boxes repeatedly. Especiallyif some emergencies happen, the pipeline will be pulled back, more cycles will besuffered. Under these cyclic loadings, the crack will grow. It will be very dangerousif the final crack growth exceeds the safety standard.

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Geometry

Based on the typical way of modeling the buckle arrestor, a simplified model iscreated in Abaqus(6.14). The pipe and the buckle arrestor are modeled with the2-nodes beam elements(B21), the cross section properties are presented in Table 2.3,thick wall pipe is adopted. The steel grade is X65, and the material is elastic-perfectplastic. The true stress-strain curve is used in the analysis. And the steel densitywill be used in gravity.

Table 2.3: Pipe Section Properties

Pipe Section Tapper Section Buckle ArrestorDiameter 0.8128 m 0.8478 m 0.8828 mWall Thickness 0.039 m 0.057 m 0.074 mLength 0.14 m 3.32 m

The stinger profile is modeled under a perfect radius of 140 m, nearly every 8 malong the circumference a roller-box is positioned. Seven roller-boxes are taken intoaccount, they are modeled as the rigid circles with the radius of 0.3 m. As for thecontact properties, in the tangent direction, it is frictionless; in the normal direction,a linear contact stiffness of 70000 kN/m is assigned.

Boundary Conditions

For the boundary conditions, the rollers are completely fixed, no displacements androtations are allowed. The right end of the pipe is totally fixed, external loads areadded on the left end, as present in Figure 2.4.

Loading Steps

First, the tension of 7000 kN is added on the left end of pipe, and it is allowed tofollow the rotation in the following loading steps.

Second, according to the departure angle, the equivalent rotation angle is addedon the left end of pipe, mainly to let pipe fit the stinger profile. The magnitude ofthe tension will not be changed, while its direction will follow the rotation.

Third, the effective gravity forces are added on different sections. Because the modelis built up under Standard/Explicit Model, the static buoyancy can not be addeddirectly. Assuming that the empty pipe sections are fully submerged in water, grav-ity and buoyancy are combined together by calculating the effective accelerationsof pipe sections, tapper sections, and buckle arrestor respectively. The calculationmethods are described below.

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Weight per unit length in air:

Wair = π ∗

((Do

2

)2

−(Do − 2t

2

)2)∗ ρsteel

Submerged Weight per unit length:

Wsub = Wair − ρsea ∗ g ∗ π ∗(Do

2

)2

Mass per unit length:

M =π

4∗D2

o − (Do − 2t)2 ∗ ρsteelg

Effective acceleration:

geff =Wsub

M

Here Do is the outside diameter, t is the wall thickness.

In order to model the pipe sections conveniently, the whole stinger profile has beenrotated 17 ◦ in clockwise direction at the beginning. The reason is that, the modelis made reference from a pipe-lay vessel, under the global coordinate, the tangen-tial direction of the first roller is not in horizontal. While the effective gravity isadded under the local coordinate. So the obtained effective accelerations which isbased on the global coordinate must be decomposed in x-direction and y-directionrespectively. The tension and rotation are maintained the same. The decomposedeffective accelerations are added in the third stage.

Base Case

In order to avoid the influence of the pipe right end boundary conditions, the investi-gated positions start from the third roller to the sixth roller which corresponding tothe departure roller. The buckle arrestor is positioned on these rollers and betweenthese rollers respectively. Examples are presented in Figure 2.4 and Figure 2.5.

2.2.2 Modeling with Time Loading History

When the buckle arrestor passes over the stinger, it goes on and drops off the roller-boxes repeatedly. In order to study its behavior under the cyclic loading situation,a new model is developed by modifying the base model.

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Figure 2.4: Buckle Arrestor on the Third Roller

Figure 2.5: Buckle Arrestor between the Third and the Fourth Roller

First Step

The pipe sections with the buckle arrestor are maintained at unloading state. Asupplementary pipe section is added on the right side of the first roller, see in Fig-ure 2.6. This supplementary section is restricted by a group of fixed rollers whichare located at both top and bottom positions. Similarly when defining the contactproperties of these rollers, in the tangent direction, it is frictionless; in the normaldirection, the contact stiffness is 70000 kN/m. The main objective of these rollersis to restrict the vertical displacements and rotations of the supplementary sectionwhen the buckle arrestor moves along the stinger. The right end of feeding sectionis restrained in the displacement of y-direction. The rotation around z-axis is re-strained as well. So the supplementary section is allowed to move only in x-directionduring later loading steps.

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Figure 2.6: Initial State

Second Step

The procedures are similar to the base model. The tension, rotation and effectivegravity are applied step by step. The pipe sections is draped on the stinger, see theFigure 2.7

Figure 2.7: Drape Pipe on Stinger

Third Step

The buckle arrestor is forced to move along the stinger profile under proper timeloading history. At the left end, the original draped pipe slides off the stinger. Atthe right end, new pipe sections are continuously supplemented. The procedurelooks like installing pipe.

Both loading control method and displacement control method have been applied.Through the simulation, it was found out that the loading control method is not

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appropriate. Because it is hard to adjust the balance between tension and bendingmoment. As a result, the buckle arrestor could not follow the stinger profile prop-erly. So the displacement control method is adopted here, the mainly objective isto maintain the curvature of pipe sections during its passage over the stinger.

Figure 2.8: Buckle Arrestor Move to the Departure Roller

During the simulation, every 2s, the right end of pipe is moved 0.2 m towards leftdirection. Meanwhile, the rotation angle at the pipe left end is increased by 0.0015radians, mainly to maintain the departure angle. Under this loading procedure, thebuckle arrestor moves along the stinger profile smoothly. It goes on the rollers anddrops off the rollers step by step till the departure roller, as shown in Figure 2.8.According to the results in Figure 2.8, the strain at the supplementary section isreally small which means that it has hardly any influence on the buckle arrestorpart, so the modeling method is reasonable.

2.2.3 Simulation Results

Base Model

Several cases have been performed, the buckle arrestor is positioned on differentlocations. Figure 2.9 and Figure 2.10 are examples which show the longitudinalstrain variation along the pipe sections when the buckle arrestor is located on theroller and between the rollers respectively.

When the buckle arrestor is located on the rollers, at the both side of the bucklearrestor, there are strain intensification on the pipe sections. The largest strainintensification appears at the sixth roller. While when buckle arrestor is locatedbetween the rollers, the strain intensification reduces. The relevant strain values ofthese two situations are summarized in Table 2.4.

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Figure 2.9: Strain Variation-Buckle Arrestor on the Third Roller

Figure 2.10: Strain Variation-Buckle Arrestor between the Third and Fourth Rollers

Table 2.4: Strain at Girth Welding Part

On the rollers 3rd 4th 5th 6thStrain (%) 0.48 0.48 0.48 0.5Between the Rollers 3rd-4th 4th-5th 5th-6thStrain (%) 0.43 0.43 0.43

Moving Model

The simulation results are presented as follows. Figure 2.11 shows the strain vari-ation of a element which is selected from the strain intensification area under thetime loading history.

As reflected from the graph, the strains almost keeps the same level when the bucklearrestor moves on the rollers or moves between rollers respectively. These also reflectthat added loading history is reasonable since it maintains appropriate curvaturesof the buckle arrestor. When the buckle arrestor is located on the sixth roller, the

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Figure 2.11: Longitudinal Strain(Girth Welding) under Time Loading History

strain will be higher. Table 2.5 summarizes the results.

Table 2.5: Strain at Girth Welding Part

On the rollers 3rd 4th 5th 6thStrain (%) 0.52 0.52 0.52 0.55Between the Rollers 3rd-4th 4th-5th 5th-6thStrain (%) 0.5 0.5 0.5

Figure 2.12: Bending Moment(Buckle Arrestor Mid Point) under Time LoadingHistory

Figure 2.12 presents the bending moment variation of a element which is picked fromthe middle of the buckle arrestor under the time loading history. When the bucklearrestor is located on the roller, the bending moment maintains around 8100 kN.m;

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when it is between the rollers, the bending moment drops to about 7000 kN.m. Atthe departure roller, the moment is bit higher, it is around 8200 kN.m. The bendingmoment variation will be used in local FE analysis.

Comparing the results of these two models, the moving model is more conserva-tive. The possible reasons are: in the new model, the total fixed end is away fromthe first roller; the gravity effects of the feeding pipe sections; in order to let thebuckle arrestor follow the stinger path, the displacement control is added strictly.

A good advantage of the new model is that, the time loading history will givebetter estimation of the cyclic loading is quite large. Especially accessing the strainwhen buckle arrestor between the roller-boxes, the strain will be smaller if it neglectsresidual strain which caused by previous plastic deformation.

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Chapter 3

Buckle Arrestor Local FE Analysis

3.1 Static Modeling Analysis

3.1.1 Former Study

In the global model, 2D beam elements are used, mainly to obtain the globalbending moment, roller reaction forces, etc. However it could not reflect the lo-cal strain/stress behavior of pipe cross section. So a more specific local FE modelhas to be made to identify the detail strain/stress behavior of pipe. The local anal-ysis results will be used in fracture assessment.

According to the study from Saipem S.p.A [1], a whole buckle arrestor with suf-ficient extended pipe sections is built. The FE model is used for the situation whenbuckle arrestor on the rollers. By adding global output into local the FE model,more specific strain intensifications along the pipe sections are obtained. It turns outthat the longitudinal strain intensifications in both left and right sides are almostthe same [1], as shown in Figure 3.1.

Figure 3.1: Longitudinal Strain Along Buckle Arrestor [1]

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3.1.2 Simplified Model

Based on the previous study, the symmetry characteristic is considered, and half ofthe buckle arrestor with extended pipe is modeled. The pipe section must be suffi-cient so that the boundary conditions of the pipe end will not influence the strainintensification area. In the local FE model, detailed geometry is considered, tappersection is added between buckle arrestor and pipe section. Solid C3D8R element isused here, and the model is detail meshed in order to grasp the strain intensificationbehavior.

The global output can be used as input of local model, tension and bending momentare added at the end of buckle arrestor. The dynamic amplification effect is consid-ered. In a conservative way, 10200 kN.m bending moment is added for the situationwhen the buckle arrestor is located on the rollers. When the buckle arrestor is posi-tioned between the rollers, the bending moment is 5000 kN.m. History effects mustbe considered, the bending moment of 10200 kN.m is added first, then the bendingmoment is unloaded to 5000 kN.m in later step. Otherwise without taking residualstrain into account, the obtained strain in the unloading stage will be much smaller.The tension is 7000 kN and it maintains the same for these two situations. The pipeend is totally fixed under conservative considerations.

The simulation results are shown in Figure 3.2 and Figure 3.3 , the graphs presentthe longitudinal strain variation under different loading scenario. From the graphs,the longitudinal strain intensification at the pipe section which is close to the bucklearrestor could reach 1.28% when the buckle arrestor is located on the rollers, and itdrops to 1.14% when the buckle arrestor is located between the rollers.

Figure 3.2: Longitudinal Strain - Buckle Arrestor on the Rollers

3.2 Cyclic Loading

Based on the global analysis, cyclic loadings are added on the local model. Theloading steps are simplified here, only considering the certain moments when bucklearrestor goes on and drops off the rollers. Because from previous global analysis,the strain variations are much smaller when the buckle arrestor moves on the rollers

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Figure 3.3: Longitudinal Strain - Buckle Arrestor between the Rollers

or the distance between two rollers. These relative small strain variations could beneglected.

The dynamic effect is taken into account, the amplified external bending momentsis applied. When buckle arrestor is located on the rollers, the moment is 10200kN.m. When it is positioned between the rollers, the moment drops to 5000 kN.m.The tension 7000 kN is maintained the same for these two cases, and it is allowed tofollow the rotation when bending moment is applied. The loads are applied for threecycles. The relevant strain and stress variations are shown in Figure 3.4 respectively.The longitudinal stress 460 MPa will be used in the later tearing analysis, while thelongitudinal stress range 250 MPa will be used in fatigue assessment.

Figure 3.4: Strain & stress under cyclic loading

Figure 3.4 illustrates the perfect plastic behavior of the material as well. During thecyclic loading, once the elastic-perfect plastic material is plastified, no more plasticdeformation will happen if the loads are not increased in the next cycle.

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Chapter 4

Theory of Engineering CriticalAssessment

4.1 Critical Concepts in Fracture Mechanics

4.1.1 J-Integral

The J-integral is based on the energy balance approach.According to the Griffith Energy Balance Theory, the total energy U of the crackedplate is [5]:

U = U0 + Ua + Uγ − Fwhere:U0 is the elastic energy of loaded non-flaw plate;Ua is the change in elastic energy induced by introducing crack in the plate;Uγ is the change in the elastic surface energy caused by the formation of the cracksurface;F is the energy caused by outside force.

Within some restrictions, the nonlinear elastic behavior of a material could be usedto describe its plastic behavior. The main restriction is that no unloading may hap-pen in anywhere of a body since in reality the plastic deformation is irreversible [5].

By definition, the J-Integral is written as:

J = −dUpda

Here the potential energy Up is defined as:

Up = U0 + Ua − F

According to the Green’s theorem, the path independent of the J-Integral expressionallows calculation along a contour remote from the crack tip. The contour can bechosen to contain only elastic loads and displacements, thus the elastic- plasticenergy release rate can be obtained though it [5].

19

Because the J-Integral is consider as an elastic-plastic energy release rate, a criticalvalue Jc is defined, which describes the characteristic of a material and predicts theonset of crack growth [5]. The calculated J values can be compared with the Jc,while J must be less than Jc in fracture assessment.

4.1.2 Crack Tip Opening Displacement

The CTOD(Crack Tip Opening Displacement) method was introduced by Wells.The crack tip stress will exceed the yield strength and this leads to plastic deforma-tion. The failure will occur when the plastic strain exceeds the limit state [5].

Wells considered that the stress near the crack tip would always reach the criti-cal value, as a result, the plastic strain in crack tip region controls fracture [5]. Ameasure of the amount of crack tip plastic strain which in terms of the displacementat the crack flanks, especially near the crack tip. Thus it was expected that at theonset of fracture the Crack Tip Opening Displacement has a critical value for itsown material, it could be used as a fracture criterion [5].

In 1966, burdekin and Stone provided an improved basis for the CTOD conceptbased on the Dugdale strip yield model. The result expression is [5]:

δt =8σya

πElnsec

(πσ

2σy

)

The equation is only valid for the infinite plate, it is not possible to derive similarequation for particular geometries, thus it is used to compare the fracture resistanceof materials.

4.1.3 Stress Intensity Approach

Due to the practical difficulties of energy balance approach, Irwin(1950s) came upwith the stress intensity approach. In the linear elastic theory, Irwin illustrated thatthe stresses near the crack tip could be express in the form [5]:

σij =K√2πr

fij(θ) + ...

where r and θ are the cylindrical polar coordinates of a point with respect to thecrack tip.

K is the stress intensity factor which describes the stress magnitude. The generalformula of the stress intensity factor is [5]:

K = σ√πaf

( aw

)where f( a

w) is a dimensionless parameter which depends on the geometries.

Irwin illustrated that if a crack grows by da, the work done by stress field in front

20

of the crack when moving through the displacements corresponding to a crack oflength(a + da) is formally equal to the change of strain energy(Gda) [5]. Thus theeffect of the stress intensity factor is similar to the energy balance approach. Besidesthe stress intensity factor can be measured experimentally. These are the reasonswhy stress intensity factor can be widely used in fracture mechanics.

Many standard industry code and some practical papers have given the solutionof intensity factor based on different flaw size, shape, specimen geometries, etc.The stress intensity factor can be applicable to stable crack extension, fatigue crackextension, stress corrosions, etc.

4.2 Method of Engineering Critical Assessment

4.2.1 General

The Engineering Critical Assessment is based on the Failure Assessment Diagramwhich is most widely used methodology for elastic-plastic fracture mechanics ofstructure components. The original FAD is derived from the strip-yield zone correc-tion, later more accurate FAD is developed from the elastic-plastic J-integral [10].The FAD approach is versatile, it can be used in brittle fracture under linear elasticconditions and ductile tearing when the loads come to plastic regime. It is alsoappropriate for the welding part since it takes residual stress into account.

In this case, the defective girth welding which is located near the buckle arrestormay fail when the series plastic loading effects exceed the material resistance. So anappropriate assessment should be performed on its strength capacity. The generalsteps are:

1. Defining the relevant loads or loading effects.2. Defining the material fracture resistance.3. Defining the ultimate crack growth.4. Accessing the crack growth under the current loading and flaw.

4.2.2 Defining Loads and Stresses

In this case, when the buckle arrestor passes over the stinger, it will go on and dropoff the roller-box in several cycles. Thus the girth welding part will suffer from shiftymembrane stresses mainly due to global bending moment changing.

When defining the loads and load effects, it contains two phases:1.Calculating the applied stress/strain without considering defective welds.2.Assess the loading effects on the defective girth welds.

21

4.2.3 Nonlinear Stress-Strain Curve

The Ramberg-Osgood equation is defined as follows:

ε =σ

E[1 + Ay

(σ

σy

)n−1

]

here σ and ε are the true stress and true strain respectively, the correspondingequations are:

σt = σ(1 + ε)

εt = ln(1 + ε)

The parameters Ay and n are defined by fitting specific points, e.g. the ultimatetensile stress and the yield point, defined as the stress at global strain equal to 0.5%[2]. According to these requirements, Ay and n are defined as:

n =log(εu−σu

E

εy−σyE

)log(σuσy

)Ay =

εyE

σy− 1

The material tensile properties should be the weakest material near the flaw [2], thischaracteristic should maintain the same in the Engineering Critical Assessment. Thestrength capacity of welds should be at least equal or even higher than the parentmaterial, the objective is to reduce local deformation with any defects.

4.2.4 Defining Fracture Resistance

The fracture toughness is converted to critical stress intensity factor, Kmat [2].When the fracture toughness is obtained from J-integral:

Kmat =

√EJmat1− υ2

Where: υ is the Poisson’s ratio.

When fracture toughness is obtained in terms of crack tip opening displacement(CTOD):

Kmat =

√mσY δmatE

1− υ2

Where:δmat is the fracture toughness in terms of CTOD;m is obtained by:

m = 1.517 ∗(σyσu

)−0.3188

for 0.3 < σyσu< 0.98, otherwise m is set to 1.5.

22

4.2.5 Characterize the Flaw Size and Shape

The initial flaw size and the maximum growth should be defined before performingECA analysis. In this cases, the flaw type is selected as surface elliptical flaw, mainlyconsidering the growth in depth direction, the maximum allowable growth is 1 mm.

4.2.6 Selection of Failure Assessment Diagram

The Failure Assessment Diagram has three alternative levels. The complexity ofthese levels are increasing due to the required material and stress analysis data [2].As a result, the accuracy will increase.

In this case, the Option-2 is selected. The failure assessment curve is defined byequation. It needs the mean uni-axial tensile true stress-strain curve at the assess-ment temperature for stresses up to σU and it is suitable for all metals regardless ofthe stress-strain behavior [2].

To derive the Option-2 curve, detailed stress-strain data are needed especially atstrain below 1%. It needs values at Lr = 0.7, 0.9, 0.98, 1.0, 1.02, 1.1, then up toLr,max [2].

For Lr < Lr,max:

f(Lr) =

(EεrefLrσy

+L3rσy

2Eεref

)−0.5

For Lr ≥ Lr,max:

f(Lr) = 0

Here the cut-off value Lr,max is calculated by:

Lr,max =σy + σu

2σy

4.2.7 Calculation of the Load Ratio Lr

The load ratio The load ratio Lr is determined via:

Lr =σrefσy

σref is the reference stress which is calculated according to BS7910-Annex P.

4.2.8 Calculation of the Fracture Ratio Kr

The fracture ratio Kr is determined via:

Kr =KI,p +KI,s

Kmat

+ ρ

23

Where:KI,p is the stress intensity factor at the current crack size due to the primary loads,see BS 7910-Annex M.KI,s is the stress intensity factor at the current crack size due to the secondary loads,see BS 7910-Annex M.ρ is used to determine the plasticity interaction effects with combined primary andsecondary loading, see BS 7910-Annex R.

The primary loads are the loads that can , if sufficiently high, contribute to fracturefailure, fatigue, creep, etc, including external loads, internal pressure [2]. The sec-ondary loads are self-equilibrating loads necessary to satisfy compatibility in struc-ture, thermal stresses and residual stresses are treated as secondary loads which donot contribute plastic collapse [2].

4.3 Ductile Tearing Analysis

4.3.1 Ductile Tearing Mechanism

Ductile crack growth usually follows three stages, micro-void initiation, voids growthnear the crack tip, voids coalescence at the tip of a existing crack [10], the Figure4.2 illustrates the mechanism.

Figure 4.1: Mechanism of Tearing Growth [10]

For a structure which contains flaws, when external loads increase to a certain level,the local stresses and strains near the crack tip are sufficient to nucleate voids. Thevoids grows gradually and finally become part of main crack, as a result, the crackgrows [10].

24

4.3.2 Ductile Tearing Instability

Ductile crack growth shows stability when the crack driving force change rate is lessthan or equal to material resistance change rate. The following equations define thetearing modulus [10].

Tapp =E

σ2

(dJ

da

)∆T

and

TR =E

σ2

dJRda

where ∆T is the remote displacement:

∆T = ∆ + CMP

where CM is the system compliance, as shown in Figure 4.2. CM influences structureinstability. CM =∞ represents dead loading which means unstable; CM = 0 meansthe other extreme displacement control, the structure is more stable [10]. The crackis unstable when Tapp > TR.

The driving force change rate at a fixed remote displacement is:(dJ

da

)∆T

=

(∂J

∂a

)P

−(∂J

∂P

)a

(∂∆

∂a

)P

[CM +

(∂∆

∂P

)a

]−1

The fracture resistance change rate is:

JR = JR(a− a0)

For the assessment of tearing stability, two alternative methods could be used, crackdriving force diagram and stability assessment diagram. Crack driving force diagramplots J and JR vs. crack length, while stability assessment diagram plots tearingmodulus vs J .

Figure 4.3 illustrates the mechanism of crack driving force diagram for both loadcontrol and displacement control. In this graph, for load control, crack is unstableat P3, while for displacement control, at ∆3 it is stable.

Figure 4.4 is a stability assessment diagram. It plot Tapp and TR against J and JRrespectively. Crack becomes unstable when the Tapp − J curve crosses the TR − JRcurve.

4.3.3 Ductile Tearing with Failure Assessment Diagram

Ductile tearing analysis can be combined with Failure Assessment Diagram. Thismethod is essentially similar to the crack driving force diagram and stability assess-ment diagram, it plots crack driving force and material fracture resistance in terms

25

Figure 4.2: A cracked structure with finite compliance [10]

of Kr and Lr [10].

In this case, the option 2 is selected to assess the ductile tearing behavior of de-fective girth welds. Several amounts of tearing crack growth are postulated, thefracture ratio Kr and the load ratio Lr are calculated based on the updated flawsize which equals to the current flaw size plus the increased crack growth [2], bothflaw size and fracture toughness should be updated as crack growth. The maximumallowable crack growth is 1mm.

In each cycle, all pairs (Lr,Kr) are functions of updated flaw size. The initial flawsize shall be evaluated at initial fracture toughness K0.2mm [2], followed by flaw sizebased on amounts of tearing growth at a fixed load.

The calculated pairs (Lr,Kr) are plotted on the FAD diagram. If the locus lineis completely located outside the FAD, the flaw is unacceptable; if the locus linecrosses the boundary of FAD, some ductile tearing could occur. Figure 4.5 shows

26

Figure 4.3: J , JR vs crack size [10]

Figure 4.4: T , TR vs J [10]

three possible results of ductile tearing assessment.

The whole analysis is based on the loading control. However the ductile tearingassessment would be conservative if the loading control are nearly close to displace-ment control [10].

27

Figure 4.5: Ductile Tearing with FAD [10]

4.4 Fatigue Crack Growth Assessment

4.4.1 Fatigue Analysis

To analysis the crack growth under fatigue loading, the general method is to esti-mate the fatigue life by integrating the crack growth law. It is allowable to use theaccurate cyclic stress intensity factor expressions and specific fatigue crack growthdata [2].

In the fatigue fracture assessment, conservative estimation of the fatigue param-eters are needed. It is assumed that an idealized flaw as a sharp tipped crack thatpropagates under the crack growth rate law, da/dN , and the range of stress intensityfactor, ∆K [2]. The general relationship between da/dN and ∆K is simplified to asigmoid curve in a log(da/dN) versus log(∆K) plot [2]. As shown in Figure 4.6.

For the corresponding equation, the Paris law is as follows:

da

dN= A ∗ (∆K)m

A and m are constants that depend on material and applied conditions, includingenvironment and cyclic frequency;

For ∆K < ∆K0, da/dN is assumed to be 0.

The stress intensity factor range, ∆K, is a function of geometry, stress range andinstantaneous crack size, and it is calculated from the following equation:

∆K = Y (∆σ) ∗√πa

28

Figure 4.6: Paris Law [2]

The general equation of Y (∆σ) is given in BS 7910 Annex M.

4.4.2 General procedure of assessment

The crack growth relationship and relevant value of ∆K0 is determined from theTable 4.4.2. For elliptical flaws, it is usually assumed that the relationship of crackgrowth in both depth and length directions is the same.

Table 4.1: Recommended fatigue crack growth threshold-∆k0

Material Environment ∆K0 N/mm1.5

Steels,includingaustenitic

Air or other nonaggres-sive environments up to100 ◦C

63

Steels,excludingaustenitic

Marine with cathodicprotection, up to 20 ◦C

63

Steels,includingaustenitic

Marine,unprotected 0

Aluminium alloysAir or other nonaggres-sive environments up to20 ◦C

21

In this case, the relevant stress range of series cyclic loading are obtained from previ-ous local FEM analysis, including membrane stress range and bending stress range.It is always necessary to estimate the worst cases.

For the assumed initial flaw, the relevant stress intensity factor range ∆K corre-sponding to the applied stress range should be estimated. The solutions of the ∆K

29

is calculated according to BS 7910 Annex-M. For the partial-thickness or embeddedflaws, ∆K should be calculated at the end of both minor and major axis of theidealized elliptical flaw[BS 7910].

For the crack growth, ∆a is estimated in one cycle from the calculated ∆K us-ing the Paris law which is determined previously. As a result, in the first cycle,the initial flaw a is increased by ∆a. Similarly, the growth of ∆c in one cycle iscalculated in the same way, while in the end, the length of flaw 2c is increased by2∆c.

For the next cycle, the initial flaw a equals to a+ ∆a, c equals to c+ ∆c, reproducethe previous procedure based on the new flaw dimensions and corresponding stressrange.

In the end, under the cycle ranges, the accumulated crack growth is calculated.If it does not exceed the limit crack growth, the flaw is regarded as acceptable,otherwise, the initial flaw is not acceptable.

30

Chapter 5

Crack Growth Estimation

5.1 Description of Simplified Method

For the tearing crack growth, when the buckle arrestor is positioned on the roller-box, due to the strain intensification at the top of girth welding part, the crack isopened and tearing growth happens. While when it is located between the roller-boxes, the strain reduces and the crack is partially closed.

In the fatigue crack growth, at the certain moments when the buckle arrestor goeson and drops off the roller-boxes, the stress variation is quite high and fast, it can beregarded as high cyclic fatigue. During the stages when the buckle arrestor passesover the roller-boxes and the distance between two roller-boxes, the dynamic effectswhich introduced by the ship motions and waves are considered. These stress vari-ations can be simplified as sinusoidal format, the cycles are sufficient while theiramplitudes are relatively low.

In a conservative way, the total crack growth ∆atot is determined by the super-positions of the tearing crack growth and the fatigue crack growth:

∆atot = ∆af + ∆at

5.2 Ductile Tearing Growth

5.2.1 General Calculation Procedure

According to the previous analyses, the girth welding part will be subjected to cyclicloading when the buckle arrestor passes over the stinger, especially the moment whenbuckle arrestor goes on the roller-boxes, the local strain at the top of girth weldingpart increases a lot. To calculate the tearing crack growth under these cyclic loadingsituation, there are three assumptions based on the fracture resistance curve whichlead to different results.

The ductile tearing growth is calculated by the combination of Failure AssessmentDiagram which specified in BS 7910. The whole calculation procedures are pro-grammed in Python.

31

Surface elliptical flaw is taken into account here, only depth growth is considered.The reason is that:

a

t=

0.002

0.039≈ 0.05

c

C=

0.025

3.86≈ 0.009

where t is the pipe wall thickness, C is the pipe circumference.The ratio in the depth direction is relatively high, therefore the crack growth mainlyhappens in the depth direction.

At the beginning, according to the initial flaw size a × c, the Kr and the Lr arecalculated respectively. The assess point (Kr,Lr) locates outside the boundary ofthe Failure Assessment Diagram which means that the current flaw is unstable.Then the a is increased by ∆a (0.01 mm), based on the updated flaw size, the newKr and Lr are calculated, the access point is compared with the Failure AssessmentDiagram again. Subsequently, the calculation procedure is reproduced cycle by cycleuntil the assess point is located at the boundary of the Failure Assessment Diagram,finally the crack is stable. The total crack growth is equal to the sum of all ∆a.

In the second cycle, initially when calculating the Kr, the stress intensity factorKI is based on the flaw size which is updated at the end of first cycle.

While for the Kmat:

Kmat =

√mσY δmatE

1− υ2

The δmat is the material fracture resistance in terms of the CTOD, and the CTODis expressed as:

CTOD = CTODinitial + C1(∆a)C2

For the determination of the CTOD, three assumptions are made, which are Mate-rial Memory R Curve, History Independent R Curve, History Dependent R Curve.They are calculated separately.

The Lr is also based on the previous end reached flaw size. The assess point (Kr,Lr)is compared with the FAD, if it is outside the diagram, the a is increased by ∆a.The similar calculations are reproduced continuously until the assess point locatesat the boundary of the FAD.

The subsequent assessment procedures maintain the same. 20 cycles are taken intoaccount and the crack growth of each cycle are added up together. If the total crack

32

growth of 20 cycles is less than the limit state 1mm, the initial flaw can be regardedas safe, otherwise it is dangerous.

5.2.2 Assumption 1 - History Independent R Curve

The history independent R curve neglects the history loading effects. Each cycle isrelatively independent which means that the previous end reached CTOD has noinfluence on the initial CTOD of the next cycle, as shown in the Figure 5.1.

Figure 5.1: History Independent R Curve [4]

The CTOD-R curve just shifts to the right side based on the previous crack growth,the initial fracture resistance maintains the same level for each cycle. 20 cycles areconsidered here. The calculations are carried out on two different flaw sizes, as pre-sented in Table 5.1 and Table 5.2.

In the tearing crack growth, the History Independent R Curve is quite conservative,the crack grows in each cycle. When the initial flaw depth is 2 mm, after 20 cycles,the crack growth is 0.7 mm. While when the initial flaw depth becomes 2.5 mm, thetotal crack growth nearly reach the maximum allowable growth, 1 mm. So if thereare much more cycles, there will be more crack growth. And if the initial flaw sizeis larger, it is easier to reach the limit state.

However this assumption is not suitable for the real situation since it totally neglectsthe loading history effects. It is similar to this situation. A group of specimens, ex-cept the initial flaw size is different, other conditions are all the same. Tearing testsare carried out on these specimens, under the same loading, definitely the specimen

33

Table 5.1: Tearing Growth - Flaw 2× 25 mm (History Independent R Curve)

Cycles Flaw Depth (mm) Depth Growth (mm)1 2 0.0292 2.029 0.0293 2.058 0.034 2.088 0.035 2.118 0.0316 2.149 0.0327 2.181 0.0328 2.213 0.0339 2.246 0.03410 2.28 0.03411 2.314 0.03512 2.349 0.03613 2.385 0.03714 2.422 0.03715 2.459 0.03816 2.497 0.03917 2.536 0.0418 2.576 0.0419 2.616 0.04120 2.657 0.042

with bigger initial flaw size will have larger crack growth.

In reality, plastic deformation is generated around the crack tip during tearinggrowth. Then under partial unloading, the crack closes a bit, there will be re-verse plastic region in front of the crack tip. The reverse plastic region could reducethe fracture resistance and lower the material yield property. However the size of theregion is small and limited, it depends on the unloading level. Even if the externalloads are total released and reverse loading is added the other plastic deformationpart which around the reverse plastic region can not go back to the initial state to-tally. So the fracture resistance reached at the end of previous cycle can not totallyreturn to original state.

5.2.3 Assumption 2 - Material Memory R Curve

The Material memory R curve is based on the history loading effects. The fractureresistance does not shift to a new origin for the next cycle. The crack driving forceobtained at the end of previous cycle must be reached at the beginning of the nextcycle, then the crack is allowed to grow under larger loading. However the materialmust be elastic - perfect plastic in this assumption. The mechanism is shown inFigure 5.2

34

Table 5.2: Tearing Growth - Flaw 2.5× 25 mm (History Independent R Curve)

Cycles Flaw Depth (mm) Depth Growth (mm)1 2.5 0.0392 2.539 0.043 2.579 0.0414 2.62 0.0415 2.661 0.0426 2.703 0.0437 2.746 0.0448 2.79 0.0459 2.835 0.04610 2.881 0.04711 2.928 0.04812 2.976 0.04913 3.025 0.0514 3.075 0.05115 3.126 0.05216 3.178 0.05317 3.231 0.05518 3.286 0.05619 3.342 0.05720 3.399 0.058

Figure 5.2: Material Memory R Curve [4]

35

From the graph, it is clear to see that during cyclic loading, the previous end reachedCTOD remains unchanged; for the next cycle, only when larger crack driving forceis applied, further tearing growth will happen. The calculation results are shownin Table 5.3. In the Material Memory R Curve, the assumption of perfect elastic-

Table 5.3: Tearing Growth - Flaw 2× 25 mm (Material Memory R Curve)

Cycles Flaw Depth (mm) Depth Growth (mm)1 2 0.029

plastic material property is made, and there is no change in the material propertyunder the loading history. In the first cycle, the judge point is located outside theFailure Assessment Diagram which means the initial flaw is unstable, then the tear-ing growth happens until the crack is stable when the assess point is located at theboundary of Failure Assessment Diagram, as plotted in Figure 5.3, the red line isthe local assessment line.

Figure 5.3: Failure Assess Diagram-One Cycle

Under this assumption, the fracture resistance reached at the end of first cyclemaintains the same level for the beginning of second cycle. So in these two cer-tain moments, the flaw size, the fracture resistance, the external loads and materialproperty are all the same. As a result, the calculated Kr and Lr are equal, the judgepoint still locates at the boundary of Failure Assessment Diagram, crack is stable.Subsequently, in the following cycles, no any further tearing crack growth appear,unless the external stress increases.

In reality, the perfect elastic-plastic material does not exist. Under the cyclic load-ing, especially when large plastic deformation generates, the material property and

36

fracture property will be changed locally. Especially when the load ratio is negative(reverse loading), the reduction of the fracture resistance becomes more pronounced[9]. Thus in the later cycles, tearing crack growth may happen.

5.2.4 Assumption 3 - History Dependent R Curve

It is a common sense that plastic deformation will not only change the yield andflow property, but also affect local fracture mechanisms, the initial fracture resis-tance and fatigue properties [8]. The Material Memory R Curve can not present thepre-strain history effect on the fracture resistance accurately. Because it assumesthat the material is elastic-perfect plastic, and no any change of the material frac-ture property under the plastic loading. While the History Independent R Curvetotally neglects the plastic deformation history. The History Dependent R Curve,as shown in Figure 5.4, should be evaluated properly.

Figure 5.4: History Dependent R Curve [8]

Under the cyclic plastic loading history, the initial fracture resistance of the latercycle will not drop to original state, and it will also not remain the same level asprevious cycle reached, the value will between them. It mainly depends on the un-loading level or even reverse loading.

In this case, when the buckle arrestor is positioned on the roller-boxes, the strainat girth welding part reaches around 1.28%; when it is located between the roller-boxes, the strain drop to 1.14%. Here since the reduction of fracture resistance ishard to estimate, it is assumed that the initial fracture resistance drop to 50% and

37

75% of previous end reached CTOD respectively. The relevant results are shown inthe following tables.

Table 5.4: Tearing Growth - Flaw 2× 25 mm (History Dependent R Curve)

Cycles Flaw Depth (mm) Growth (mm)1 2 0.0292 2.029 0.0143 2.043 0.0144 2.057 0.0155 2.072 0.0146 2.086 0.0157 2.101 0.0158 2.116 0.0159 2.131 0.01510 2.146 0.01511 2.161 0.01512 2.176 0.01613 2.192 0.01514 2.207 0.01615 2.223 0.01616 2.239 0.01617 2.255 0.01618 2.271 0.01619 2.287 0.01620 2.303 0.017

As reflected from the calculation results, fewer reduction of the previous end reachedfracture resistance, less crack growth happens in the subsequent cycles. The reduc-tion of the fracture resistance may depend on the unloading level or even the reverseloading, the strength of basic material, etc.

Under this assumption, the tearing crack growth happens continuously when thebuckle arrestor passes over the rollers, besides the crack growth of each cycle grad-ually increases. In real installation, if some emergency happens, the pipe is pulledback, the buckle arrestor experiences more cycles. In the end, the crack growth mayexceed the limit state which will be dangerous.

5.3 Fatigue Crack Growth

According to the Paris-Erdogan Law which is illustrated in the previous chapter andthe assumption of these loading ranges, the fatigue crack growth are carried out.According to the instructions in the BS 7910, the selected fatigue crack growth laws

38

Table 5.5: Tearing Growth - Flaw 2× 25 mm (History Dependent R Curve-75%)

Cycles Flaw Depth (mm) Growth (mm)1 2 0.0292 2.029 0.0053 2.034 0.0054 2.039 0.0055 2.044 0.0056 2.049 0.0067 2.055 0.0068 2.061 0.0069 2.067 0.00610 2.073 0.00611 2.079 0.00612 2.085 0.00613 2.091 0.00614 2.097 0.00615 2.103 0.00616 2.109 0.00617 2.115 0.00618 2.121 0.00619 2.127 0.00620 2.133 0.006

are presented in Table 5.6. The calculation procedures are achieved in the Python.The Table 5.7 presents the results.

Table 5.6: Fatigue Crack Growth -Constants

Stage ∆K N/mm3/2 m AA 63 5.1 2.1× 10−17

B 144 2.88 1.29× 10−12

Table 5.7: Fatigue Crack Growth - Flaw 2× 25 mm

Type Cycles ∆σ[MPa] Initial Flaw a× c[mm] Final Flaw a× c[mm]1 20 250 2× 25 2.009× 25.00642 400 50 2× 25 2.002× 25.001

It is obvious that when the buckle arrestor passes over the whole stinger, even if allpossible fatigue loading are taken into account, the contributions of fatigue crack

39

growth in both depth direction and length are relatively small, this is mainly dueto the limited cycles. Thus the fatigue crack growth almost can be neglected in thiscase.

40

Chapter 6

Literature Review and ResultsAnalysis

6.1 Previous FEM Research

The effects of pre-strain history on the fracture resistance have been conducted insome FEM researches. P.A. Eikrem and Z.L.Zhang have carried out the relevantnumerical research to study how a reeling induced pre-strain history affects the frac-ture resistance of an existing crack [8].

In their study, a complete Gurson model was developed for the ductile tearing anal-ysis, by combining the Gurson-Tvergaard-Needleman model with the Thomason’splastic limit load model.

The yield function of the Gurson-Tvergaard-Needleman model [8]:

φ(q, σf , f∗, σm) =

q2

σ2f

+ 2q1f∗cosh(

3q2σm2σf

)− 1− (q1f∗)2

Where:f ∗ is the void volume fraction;σm is the mean stress;q is the von Mises stress;σf is the flow stress;q1 and q2 are parameters introduced by Tvergaard to modify the original Gursonmodel.

The void volume fraction is defined as:For f ≤ fc,

f ∗ = f

For fc ≤ f ≤ ff ,

f ∗ = fc + (f − fc)fu − fcff − fc

For ff ≤ f ,f ∗ = fu

41

The Thomason’s plastic limit load criterion [8] is used to determine the critical vol-ume fraction fc. Under this modification, the fc is not a input parameter anymore,it is the result of plastic deformation.

σ1

σf=

0.3

r/(R− r)+ 0.6

Where:σ1 is the maximum principle stress;r and R are current average void radius and intervoid distance which can be calcu-lated from the current principle strains.

2D single edge notched tension(SENT) specimens were used in Abaqus modeling.The void growth is only allowed under tensile deformation and during compressionit is suppressed, no element is allowed to fail completely during plastic deformation.Using nominal strain which is defined by the ratio of applied displacement dividedby the initial length as external loading parameters [8]. Both symmetrical and non-symmetrical pre-strain cycles are investigated, as presented in Figure 6.1, Figure6.2, Figure 6.3, and Figure 6.4.

Figure 6.1: CTOD vs Different Symmetrical Pre-strain Cycles [8]

From the upper figures, for the symmetrical pre-strain loading, a pre-strain up to0.2% could already reduce both the initial fracture toughness and crack growth re-sistance for the following cycles. When pre-strain reaches 0.3%, the initial fractureresistance is nearly equal to zero for the next loading step, this means that the crackgrowth starts at the beginning of the next tensile loading step.

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Figure 6.2: Effects of Different Symmetrical Pre-strain on the Fracture Resistance[8]

Figure 6.3: CTOD vs Different Non-symmetrical Pre-strain Cycles [8]

As reflected from the figures, in the non-symmetrical pre-strain cases, the crackgrowth happened under the pre-strain loading. The CTOD reached at the end ofpre-tension will be reduced once the compressive loading is added. Thus in the nextloading stage, the crack growth will start at a CTOD which is higher than the initialCTOD of the monotonic loading, but lower than the pre-tension end CTOD.

The pre-strain loading history could influence the initial fracture resistance of the

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Figure 6.4: Effects of Different Non-symmetrical Pre-strain on the Fracture Resis-tance [8]

next loading stage, especially when high compressive loading is added in the pre-vious cycle. While as mentioned in the study, the model neglects the change inthe material property and stress redistribution, only small pre-strain amplitude andsingle pre-strain cycle are considered. In reality, during installation, more cyclesexist and strain amplitude is larger, the behavior of material fracture resistance,failure mechanisms and failure modes need to be investigated through systematicexperiments [8].

6.2 Similar Experiments Study

6.2.1 Case One

Experiment Overview

Tenaris, CSM and Saipem launched a series of experiments aimed at evaluating thein-service flaw acceptabilities of girth welded seamless pipes produced by Tenarisfor offshore applications [7]. The objectives of the research are:-Evaluate the tolerability of defective girth weld;-Update the experiment data of girth weld tolerance under in-service conditions;-Evaluate the applicability of ECA tools.

Experiment scenario

The applied strain are under full scale testing:-High internal pressure – simulate real operation situation;-One high plastic tensile strain ε1 – accidental load;-Cyclic limited strain range ∆ε – thermal-induced loading at shut down during

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service life.

Figure 6.5: Applied Strain Mechanism [7]

Full Scale Testing

The pipe geometry, loading scenarios, notches configurations of the four groups testare present in Table 6.1

Results Summary and Analysis

The full scale test results are summarized in Figure 6.6.

Figure 6.6: Full Scale Test Results [7]

For the first group test, according to the Figure 6.5, at the beginning, the total strain

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Table 6.1: Characteristics of Full Scale Testing [7]

No.1 No.2 No.3 No.4Outside Diameter (mm)

296.5 296.5 296.5 273Wall Thickness (mm)

21.2 21.2 21.2 15.9Internal Pressure-Hoop Stress

60% SMYS 60% SMYS 60% SMYS 60% SMYSTotal Axial Strain (%)

1.0 1.0 1.0 1.0Strain Range (%)

0.3 0.5 0.5 0.5Number of Cycles

200 200 200 till failureFlaw size (mm)

3 × 25 3 × 25 3 × 25 3 ×25Weld Characteristic

1 flaw per weld,HAZ/FL,ID surface

1 flaw per weld,WCL,

OD surface

2 flaws per weld,1 in WCL,

1 in HAZ/FL,OD surface

1st flawHAZ/FL,

2nd flawHAZ/FL weldcap removal,

3rd flawWCL weld capremoval

increase to 1%, then the cyclic loading range 0.3% is added. When performing theECA, in the first cycle, the total strain is used to calculated the tearing growth; inthe subsequent cycles, the strain range is used in fatigue growth. The calculationsare based on the BS 7910, the tearing growth is 0.27 mm, the fatigue growth is0.36 mm, so the total crack growth is 0.63 mm [7]. Compared with the experimentsresults, the average total growth is 0.43 mm, the maximum total growth is 0.50mm. Though the ECA results is slightly conservative, it is applicable to this kindof loading regime.

While for the other group tests, the strain range is 0.5%, it involves quite largeplastic deformation, higher compressive loading is added, no any well-defined andcommon recognized assessment procedure exist at present [7]. The experimentsresults could be used for future relevant research study.

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6.2.2 Case Two

Experiment Overview

P.K.Singh, V.R.Ranganath, etc. launched a series of experiments to study the ef-fect of cyclic loading on the elastic-plastic fracture resistance of the primary heattransport system piping material of pressurized heavy water reactors [9].

The cyclic J-R curve tests are carried out on CT specimen, quasi-static loadingconditions are conducted. In the first cycle, the pre-cracked specimen is loaded tothe pre-determined load line displacement(LLD) and then unloaded to the pointwhich is based on the specified load ratio [9]. In the next cycle, the loading is addedto an increased LLD, then it is unloaded to such a point to maintain the load ratio.The loading procedure is repeated in sufficient cycles to determine the J-R curve.The loading scheme is shown in Figure 6.7.

Figure 6.7: Cyclic Loading Scheme [9]

Experiment Results

Systematic experiments are carried out to study the effect of load ratio and theeffect of incremental plastic displacement. The effects of load ratio on the materialfracture resistance are shown in Figure 6.8 and Figure 6.9.

From the figures, it is observed that under the specific plastic displacement incre-ment, the J-R curve at load ratios of 0.8 and 0 are almost equal; while when the loadratio becomes negative, especially when the load ratio approaches -1, the materialfracture resistance drops a lot. This means that under cyclic loading, the increasedcompressive load could decrease the material strength capacity which in terms offracture resistance.

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Figure 6.8: Fracture Resistance vs Load ratio (δ = 0.3 mm) [9]

Figure 6.9: Fracture Resistance vs Load ratio (δ = 0.5 mm) [9]

Experiment Conclusions

Cyclic loading can reduce the material fracture resistance compared to monotonicloading, especially the load ratio becomes negative.

An obvious observation is that, large crack tip blunting is observed under monotonicloading. However when the loading becomes cyclic, especially under a negative load-ing ratio, at the crack tip, more voids are sharpened due to the alternating tensileand compressive stresses [9]. As a result, it facilities the voids coalescence. Andhence there is reduction on the fracture resistance at the crack tip region.

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So under cyclic loading, if the load ratio is no less than zero, the fracture resis-tance will not be influenced. The tearing crack growth and fatigue crack growthcan be treated separately and superposed in the end. While if the loading ratio be-comes negative, the fracture resistance will be decreased. Especially near the cracktip, larger reverse plasticity zone will generate, the simplified superposition methodis not suitable anymore, the mutual effects between the cyclic fracture resistancedegradation and fatigue crack propagation should be careful considered [9].

6.3 Results Analysis

According to the previous FE study and the similar experiments, the analysis ofthis case is discussed below.

When the buckle arrestor goes on the first roller, the longitudinal strain at girthwelding 12 o’clock position reaches 1.28%, ductile tearing growth happens. Basedon the ECA, the predicted tearing crack growth in depth direction is 0.029 mm.

After that the buckle arrestor drops off and goes on the rollers repeatedly. Duringthe cyclic loading, the reduction of the longitudinal strain is around 0.15% which isrelatively small. So the reached CTOD will not be decreased during the later cyclicloading, no further tearing happens. For the later cycles, the accumulated fatiguecrack growth is around 0.011 mm.

The final crack growth in depth direction can be treated as superposition of tearingcrack growth and fatigue crack growth. It is about 0.04 mm which is within limitstate. So the buckle arrestor will be safe under the current flaw size.

6.4 Future FE Study Proposal

6.4.1 Global Physics Summary

In the global physics point of view, when assessing the crack propagation, the threebasic factors are: the crack driving force, the material fracture resistance, and thecrack size.

For a defective structure, 1% strain is applied in the first cycle, tearing growthhappens. During this stage, the applied crack driving force is compared with thefracture resistance curve which is usually obtained under the monotonic testing.Then in the following cycles, large cyclic strain range is acted on the flaw, as provedin experiments and FE simulation, high negative loading ratio could reduce the ma-terial fracture resistance.

In the later cycle, if the strain range is large enough, which means that the highnegative loading ratio is applied. As a result, the degradation on the fracture re-sistance could cause further tearing growth. So the simplified superposition is notsuitable anymore. The mutual effects between the ductile tearing and fatigue need

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to be evaluated properly.

6.4.2 FE study Proposal

Gurson Model

Ductile fracture is the result of micro voids nucleation, growth and coalescence. Thebest known model is originally developed by Gurson and later modified by Tver-gaard and Needleman. The Gurson model is a void growth model, by introducingthe damage variable D into the void volume fraction. However the model is lackof a physical mechanism-based coalescence criterion [8]. Zhang et al. proposed acomplete Gurson model by combining the GTN model with the Thomason’s plasticlimit load criterion [8]. An advantage of the complete Gurson model is that thecritical volume fraction is not a material parameter anymore, it is determined bythe plastic-limit load [8].

In previous Zhang et al. [8] FE study, the complete Gruson model is used to sim-ulate the material fracture resistance under the pre-strain history. It is found outthat the CTOD is influenced by the pre-strain history. Especially when the largecompressive loading is added, there is degradation on the CTOD. As a consequence,further tearing growth happens in the next cycle. This FE simulation results aresimilar to the experiments which is conducted by P.K.Singh et al.[9].

In the fracture resistance testing, i.e. the monotonic testing, the resistance is mea-sured under the stable crack growth situation, which means that the crack drivingforce rate is equal to the fracture resistance change rate. Thus in the FE simulation,within the stable condition, the obtained applied fracture resistance can be regardedas the material fracture resistance.

In Zhang et al. FE simulation, tearing growth happens when the large tensilestrain is applied, the fracture resistance increases. After that during the unloadingprocedure, near the crack tip, the reverse plastic zone generates, as shown in Figure6.10. Thus the calculated applied fracture resistance Japp is reduced due to the pres-ence of the reverse plasticity. The higher compressive loading is applied, the lowerfracture resistance will be obtained. Also due to the existence the reverse plasticzone, higher stress will be applied at the crack tip in the next cycle. So furthertearing growth will happen in the next cycle.

In the future study, a FE study can be carried out based on the complete Gur-son model [8] with the combination of the corresponding experiments. More cycleswill be introduced to study the fracture resistance behavior under the large cyclicloading. Meanwhile the crack growth under the cyclic loading can be estimatedthrough the FE simulation. All these procedure should be done under the stablecrack growth condition. Otherwise the predicted fracture resistance curve will notbe correct.

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Figure 6.10: Deformation at the crack tip during cyclic loading [10]

Cohesive Zone in Combination with Gurson Model

The crack propagation can also modeled by combining the cohesive zone with theGurson model, as shown in Figure 6.11. The Gurson model is used to describe thematerial behavior, the cohesive zone is used to model the crack propagation.

In the FE model, when defining the cohesive law, a master curve is applied initially,as shown in Figure 6.12. At the beginning, large strain is applied, and the crackgrows. During the unloading stage, at the reverse plastic zone, there is degradationon the corresponding cohesive law. So in the next cycle, the cohesive law at thereverse plastic zone will follow another curve which has a lower bound. As for thedegradation level, it is depend on the corresponding experiments.

The main idea of this FE model is to introduce the damage of the cohesive lawto simulate the degradation of the fracture toughness at the reverse plastic zone.Though it can be realized by coupling the experiments data. However it is lack ofphysical meaning. Especially for the cohesive zone, it is more like a phenomeno-logical model. Because the Gurson model can already present the ductile fracturefailure mechanism. Also in reality, the crack propagation route is hard to predict.

While this model can be used to model the ductile-brittle transition region. In Ger-alf Hutter et al.[6] study, the Gurson model is used to describe the ductile failuremechanism, and the cohesive zone is used to model the cleavage fracture mecha-

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Figure 6.11: Model of crack propagation with cohesive zone and Gurson model [6]

Figure 6.12: Cohesive Law [6]

nism. It is used to study the effects of the temperature on the fracture toughness.Because when the temperature is low, the cleavage failure contributes more; whenthe temperature is high, the ductile fracture becomes dominant.

In the present case, the cleavage fracture is not expected. The main objective isto model the ductile fracture under the large cyclic loading. The most suitablemodel for the ductile damage is the Gurson model. So the combination of the Gur-son model and the cohesive zone is lack of physical meaning. Also the combinationmethod could introduce more difficulties during the modeling, like the boundaryconditions, mesh size, etc.

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Chapter 7

Conclusions

A systematic study has been carried out on the buckle arrestor during its passageover the stinger, the main conclusions are summarized below.

A modified global FE model is implemented by using the displacement controlmethod, and the result is similar to the static base model. However it gives betterdescriptions of the bending moment, the strain and the stress variations under aproper time loading history. Especially when the buckle arrestor suffers from thelarge cyclic loading, the typical static model will neglect the previous plastic defor-mation.

According to the previous similar FE study and the experiments, a common charac-teristic is found. During the cyclic loading, near the crack tip, the fracture resistancewill be reduced if large compressive loading is added. The loading history effects onthe fracture resistance should be considered. In this case, the cyclic loading rangeis relatively small. So the reached material fracture resistance remains unchangedin later cycles. No further ductile tearing growth happens and only fatigue crackgrowth is considered. In the end, the buckle arrestor will be safe during its passageover the stinger.

For a defective ductile structure under the cyclic loading, an accidental load couldintroduce tearing crack growth. While if cyclic loading range is relatively small,no large compressive loading is added, then no further tearing will happen in latercycles. The total crack growth can be regarded as the superposition of the tearinggrowth and fatigue growth. The present ECA can be used to predict the crackgrowth. If the cyclic strain range is quite large, for example a 0.5% strain range, thesimplified superposition is not suitable anymore, the degradation on the materialfracture resistance should be properly evaluated.

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[2] BS 7910. Guide to methods for assessing the acceptability of flaws in metallicstructures. 2013.

[3] DNV-OS-F101. Submarine Pipeline System. 2012.

[4] Ernst H. and Bravo RE et al., eds. Strain history effects on fracture mechanicsparameters-application to reeling. Proceedings of the OMAE 2005. Halkidiki,Greece, 2005.

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[6] Geralf Hutter and Thomas Linse et al. “A Modeling Approach for the Com-plete Ductile-brittle Transition Region: Cohesive Zone in Combination witha Non-local Gurson-model”. In: International Journal of Fracture 185 (2014),pp. 129–153.

[7] Giorgio Melis and Israel Marines-Garcia et al., eds. Updates on Flaw Tolera-bility and Life of Offshore Double Joints in Strain-Based Loading Conditions.Proceedings of the Twenty-fifth International Ocean and Polar EngineeringConference. Kona, Big Island, Hawaii, USA, 2015.

[8] P.A.Eikrem and Z.L.Zhang et al. “Numerical study on the effect of prestrainhistory on ductile fracture resistance by using complete Gurson model”. In:Engineering Fracture Mechanics 75 (2008), pp. 4568–4582.

[9] P.K.Singh and V.R.Ranganath et al. “Effect of cyclic loading on elastic-plasticfracture resistance of PHT system piping material of PHWR”. In: Interna-tional Journal of Pressure Vessel and Piping 80 (2003), pp. 745–752.

[10] T.L.Anderson. Fracture Mechanics. Fundamentals and Applications. 2005.

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